Joes Mutual Funds, Inc. located in Pittsburgh. Joes just obtained $10,000,000 by converting industrial bonds to cash and is now looking for other investment opportunities for these funds. Based on Joes current investments, the firms top financial analyst recommends that all new investments be made in the oil industry, steel industry, or government bonds in US and Europe. The investments, locations and rates of return are shown in the following table.

Investment Opportunities for Joes Mutual Funds

Location	Investment	Projected Rate of Return %
Pittsburgh	B&E Steel Oakland Oil Pittsburgh Steel	7.3 8.6 6.8
New York City	Atlantic Oil Pacific Oil Huber Steel Midwest Steel Government Bonds	8.9 10.5 6.8 6.5 4.5
Europe	Buckingham Steel Eiffel Oil Florence Oil EU Government Bonds	8.2 7.2 7.6 5.3

What portfolio recommendations investments and amounts should be made for the available $10,000,000 to maximize the projected rate of return? Please note that you need to develop two mathematical models (two separate excel spreadsheet) for part a and b.

a. The budgetary and managerially imposed constraints are listed below

- Joes should be investing all available $10,000,000.

- The Europe investments cannot exceed the 30% of the overall budget.

- Total Oil Investments cannot exceed the 50% of the total budget.

- Total Steel Investments cannot exceed the 50% of the total budget.

- Joes should invest on Pittsburgh funds at least 20% of the budget.

- Joes should invest on New York City funds at least 25% of the total budget.

- Joes should invest on Europe funds at least 15% of the total budget.

- At most 15% of the budget can be spent on government bonds.

- Oil sector investments in Europe should be more than Steel sector investments in Europe.

In your report, please include your mathematical model, excel output, and list the amount of investments for each investment opportunity in a table and interpret your findings.

b. The upper management of Joes Mutual Funds also considering another scenario with the following budgetary and managerially imposed constraints

- Joes should be investing all available $10,000,000.

- The Europe investments cannot exceed the 20% of the overall budget.

- Total Oil Investments cannot exceed the 30% of the total budget.

- Total Steel Investments cannot exceed the 50% of the total budget.

- Joes should invest on Pittsburgh funds at least 50% of the budget.

- Joes should invest on New York City funds at least 25% of the total budget.

- Joes should invest on Europe funds at least 15% of the total budget.

- At most 45% of the budget can be spent on government bonds.

- Oil sector investments in Europe should be less than Steel sector investments in Europe.

In your report, please include your mathematical model, excel output, and list the amount of investments for each investment opportunity in a table and interpret your findings.